The first glitch is that Mandalore's battle armor shows up as regular battle armor.

The second glitch is pretty bad, After talking with Daemon Drexel on the bridge, the battle with the Republic Admiral begins. The screen is Dark and I can't very far. I've tried reloading the module numerous times, but nothing seems to work.

If you're trying to equip the battle armour on a female character, then you need to read the known bugs section of the Read-Me.

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Could you provide more details about the second bug. So you speak to Daemon Drexl, then it fades out and warps to another module?